Representation for the W-weighted Drazin inverse of linear operators

2009 ◽  
Vol 34 (1-2) ◽  
pp. 317-328 ◽  
Author(s):  
Xiaoji Liu ◽  
Jin Zhong ◽  
Yaoming Yu
Keyword(s):  
Linear Operators ◽  
Drazin Inverse ◽  
Weighted Drazin Inverse

scholarly journals A note on the perturbation bounds of W-weighted Drazin inverse of linear operator in Banach space

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 505-511 ◽  
Author(s):  
Xue-Zhong Wang ◽  
Hai-Feng Ma ◽  
Marija Cvetkovic
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Banach Spaces ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Perturbation Bound ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Perturbation Bounds ◽  
Weighted Drazin Inverse

We investigate the perturbation bound of the W-weighted Drazin inverse for bounded linear operators between Banach spaces and present two explicit expressions for the W-weighted Drazin inverse of bounded linear operators in Banach space, which extend the results in Chin. Anna. Math., 21C:1 (2000) 39-44 by Wei.

scholarly journals The weighted g-Drazin inverse for operators

2007 ◽  
Vol 82 (2) ◽  
pp. 163-181 ◽  
Author(s):  
A. Dajić ◽  
J. J. Koliha
Keyword(s):  
Banach Spaces ◽  
Linear Algebra ◽  
Open Problem ◽  
Matrix Representation ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Operator Matrix ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Weighted Drazin Inverse

AbstractThe paper introduces and studies the weighted g-Drazin inverse for bounded linear operators between Banach spaces, extending the concept of the weighted Drazin inverse of Rakočević and Wei (Linear Algebra Appl. 350 (2002), 25–39) and of Cline and Greville (Linear Algebra Appl. 29 (1980), 53–62). We use the Mbekhta decomposition to study the structure of an operator possessing the weighted g-Drazin inverse, give an operator matrix representation for the inverse, and study its continuity. An open problem of Rakočević and Wei is solved.

scholarly journals The Weighted g-drazin inverse for operators

2006 ◽  
Vol 81 (3) ◽  
pp. 405-423 ◽  
Author(s):  
A. Dajić ◽  
J. J. Koliha
Keyword(s):  
Banach Spaces ◽  
Linear Algebra ◽  
Open Problem ◽  
Matrix Representation ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Operator Matrix ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Weighted Drazin Inverse

AbstractThe paper introduces and studies the weighted g-Drazin inverse for bounded linear operators between Banach spaces, extending the concept of the weighted Drazin inverse of Rakočević and Wei (Linear Algebra Appl. 350 (2002), 25–39) and of Cline and Greville (Linear Algebra Appl. 29(1980), 53–62). We use the Mbekhta decomposition to study the structure of an operator possessing the weighted g-Drazin inverse, give an operator matrix representation for the inverse, and study its continuity. An open problem of Rakočević and Wei is solved.

Cline’s formula for g-Drazin inverses in a ring

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2249-2255
Author(s):  
Huanyin Chen ◽  
Marjan Abdolyousefi
Keyword(s):  
Operator Theory ◽  
Spectral Properties ◽  
Associative Ring ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cline’S Formula

It is well known that for an associative ring R, if ab has g-Drazin inverse then ba has g-Drazin inverse. In this case, (ba)d = b((ab)d)2a. This formula is so-called Cline?s formula for g-Drazin inverse, which plays an elementary role in matrix and operator theory. In this paper, we generalize Cline?s formula to the wider case. In particular, as applications, we obtain new common spectral properties of bounded linear operators.

Recurrent neural network for computing the W -weighted Drazin inverse

2017 ◽  
Vol 300 ◽  
pp. 1-20 ◽  
Author(s):  
Xue-Zhong Wang ◽  
Haifeng Ma ◽  
Predrag S. Stanimirović
Keyword(s):  
Neural Network ◽  
Recurrent Neural Network ◽  
Drazin Inverse ◽  
Weighted Drazin Inverse

Common spectral properties of linear operators A and B satisfying AkBkAk = Ak+1 and BkAkBk = Bk+1

2019 ◽  
Vol 12 (05) ◽  
pp. 1950084
Author(s):  
Anuradha Gupta ◽  
Ankit Kumar
Keyword(s):  
Banach Space ◽  
Positive Integer ◽  
Spectral Properties ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cline’S Formula

Let [Formula: see text] and [Formula: see text] be two bounded linear operators on a Banach space [Formula: see text] and [Formula: see text] be a positive integer such that [Formula: see text] and [Formula: see text], then [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] have some common spectral properties. Drazin invertibility and polaroidness of these operators are also discussed. Cline’s formula for Drazin inverse in a ring with identity is also studied under the assumption that [Formula: see text] for some positive integer [Formula: see text].

On the Generalized Drazin Inverse of the Sum of Two Operators

2013 ◽  
Vol 846-847 ◽  
pp. 1286-1290
Author(s):  
Shi Qiang Wang ◽  
Li Guo ◽  
Lei Zhang
Keyword(s):  
Banach Space ◽  
Explicit Representation ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Generalized Drazin Inverse

In this paper, we investigate additive properties for the generalized Drazin inverse of bounded linear operators on Banach space . We give explicit representation of the generalized Drazin inverse in terms of under some conditions.

Sign in / Sign up

Export Citation Format

Share Document